Earlier quoted context omitted.
But a bug in a web-server running as root might lead to privileged execution of arbitrary code. It's certainly true that a bug in the authentication code that incorrectly grants access is of substantially less severity than a leak or abuse of root key/password.
Obviously you have to compare the likelihood of remote code execution in nginx/apache to that of ssh. Nginx is much, much simpler than OpenSSH. And, obviously, giving a third party remote root SSH access to your server already is a glaring vulnerability .
Moreover, the default SSH setup gives you everything you need for the (still undesirable) current setup, and is almost certainly running regardless. The default nginx install does not - you have to tweak setup to lock it down and add stuff to actually fetch the content, and since that (we have stipulated) has to be done as a privileged user there is room for error.
Again, giving a root login key to OVH means no security against OVH, and relying on their securing the key. I agree that this is a bad idea. Depending on the amount you trust OVH and their security, it may be more secure against people other than OVH than certain specific alternatives (perhaps all the alternatives if you artificially constrain yourself into running a single process as root that talks to the outside).